No sequence of steps leaving 2011 blue squares
Source: Romanian MO 2010 Grade 7
August 6, 2012
combinatorics proposedcombinatorics
Problem Statement
Each of the small squares of a table is coloured in red or blue. Initially all squares are red. A step means changing the colour of all squares on a row or on a column.
a) Prove that there exists no sequence of steps, such that at the end there are exactly blue squares.
b) Describe a sequence of steps, such that at the end exactly squares are blue.Adriana & Lucian Dragomir